A coupling arrangement of the type mentioned above is known from DE 10 2012 209 477 A1. The arrangement of the torsional vibration damper adjacent to the input side of the clutch housing facing a drive and the arrangement of the clutch mechanism adjacent to an output side of the clutch housing facing a driven end leads to a possible configuration of the clutch housing in which the clutch housing is appreciably larger radially at its input side facing a drive than at its output side facing a driven end. Accordingly, with respect to its outer dimensions, the clutch housing follows the inner configuration of a transmission housing constructed in a conventional manner such that the clutch housing can be inserted axially deep into the transmission housing and accordingly requires less axial installation space. At the same time, there is sufficient installation space for the torsional vibration damper so that the latter can be constructed not only with a plurality of damper units in radial direction but, beyond this, can also still have space for installing a mass damper system. Conversely, the clutch mechanism which requires appreciably less installation space in radial direction than the torsional vibration damper fits in a spatial region of the clutch housing which allows the clutch housing to afford installation space for transmission components radially outwardly of the clutch units and radially inwardly of the clutch units. However, in the known coupling arrangement the pressing device serving to produce or cancel an operative connection between the input-side clutch units and output-side clutch units is arranged directly adjacent to the output side facing a driven end and must be supplied with flow medium via comparatively long flow paths.